Using discrete element methods, geotechnical engineers can create “virtual laboratories” to simulate conventional laboratory tests. In this study, three-dimensional DEM simulations of direct shear tests are coupled with equivalent physical tests on steel balls. The macro-scale response of simulations is compared with the physical test results to validate the discrete element model and to gain i...

In this paper, a multi-scale analysis scheme for solidification based on two-scale computational homogenization is discussed. Solidification problems involve evolution of surfaces coupled with flux jump boundary conditions across interfaces. We provide consistent macro-micro transition and averaging rules based on Hill’s macrohomogeneity condition. The overall macro-scale behavior is analyzed w...

A macro-filter-lens design that can correct for chromatic and geometric aberrations simultaneously while providing for a long focal length is presented. The filter is easy to fabricate since it involves two spherical surfaces and a planar surface. Chromatic aberration correction is achieved by making all the rays travel the same optical distance inside the filter element (negative meniscus). Ge...

in order to determine the effect of potassium silicate solution with elements of macro and micro elements on agronomic traits of rice, tarom, a field experiment in paddy fields galogah city - village marbles of the crop year 2014 was conducted. the results showed that the highest plant height (013/180 cm) to 2 liters per hectare and no interaction effects of potassium silicate elements. the res...

Macro-elements of smoothness C r on Powell-Sabin triangle splits are constructed for all r 0. These new elements are improvements on elements constructed in 10] in that certain unneeded degrees of freedom have been removed. A bivariate macro-element deened on a triangle T consists of a nite dimensional linear space S deened on T, and a set of linear functionals forming a basis for the dual of S...

Macro-elements of smoothness C r on Clough-Tocher triangle splits are constructed for all r 0. These new elements are improvements on elements constructed in 11] in that (disproving a conjecture made there) certain unneeded degrees of freedom have been removed. Numerical experiments on Hermite interpolation with the new elements are included. A bivariate macro-element deened on a triangle T con...

A C macro-element in four variables is constructed based on a split of a cross polytope into sixteen simplices. The element uses supersplines of degree nine, and provides optimal order approximation of smooth functions.

A new macro-element useful for finite element approximations to fourth order elliptic problems with curved boundaries is presented. An error analysis is given 2 which shows that these elements achieve 0(h ) accuracy in energy.